TSTP Solution File: SWC023+1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SWC023+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n011.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Tue Jul 19 22:01:09 EDT 2022

% Result   : Theorem 3.33s 3.57s
% Output   : Refutation 3.33s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   21
% Syntax   : Number of clauses     :   68 (  38 unt;  14 nHn;  68 RR)
%            Number of literals    :  129 (   0 equ;  55 neg)
%            Maximal clause size   :    7 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   13 (  12 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ssList(skc5),
    file('SWC023+1.p',unknown),
    [] ).

cnf(2,axiom,
    ssList(skc4),
    file('SWC023+1.p',unknown),
    [] ).

cnf(6,axiom,
    cyclefreeP(nil),
    file('SWC023+1.p',unknown),
    [] ).

cnf(7,axiom,
    totalorderP(nil),
    file('SWC023+1.p',unknown),
    [] ).

cnf(8,axiom,
    strictorderP(nil),
    file('SWC023+1.p',unknown),
    [] ).

cnf(9,axiom,
    totalorderedP(nil),
    file('SWC023+1.p',unknown),
    [] ).

cnf(10,axiom,
    strictorderedP(nil),
    file('SWC023+1.p',unknown),
    [] ).

cnf(11,axiom,
    duplicatefreeP(nil),
    file('SWC023+1.p',unknown),
    [] ).

cnf(12,axiom,
    equalelemsP(nil),
    file('SWC023+1.p',unknown),
    [] ).

cnf(13,axiom,
    neq(skc5,nil),
    file('SWC023+1.p',unknown),
    [] ).

cnf(52,axiom,
    ssList(skf44(u,v)),
    file('SWC023+1.p',unknown),
    [] ).

cnf(61,axiom,
    ( ~ ssList(u)
    | frontsegP(u,u) ),
    file('SWC023+1.p',unknown),
    [] ).

cnf(62,axiom,
    ( ~ ssList(u)
    | frontsegP(u,nil) ),
    file('SWC023+1.p',unknown),
    [] ).

cnf(68,axiom,
    ( ~ skP0(skc4,skc5)
    | equal(nil,skc5) ),
    file('SWC023+1.p',unknown),
    [] ).

cnf(69,axiom,
    ( ~ skP0(skc4,skc5)
    | equal(nil,skc4) ),
    file('SWC023+1.p',unknown),
    [] ).

cnf(79,axiom,
    ( skP0(u,v)
    | neq(skf44(u,v),nil) ),
    file('SWC023+1.p',unknown),
    [] ).

cnf(80,axiom,
    ( skP0(u,v)
    | frontsegP(v,skf44(u,v)) ),
    file('SWC023+1.p',unknown),
    [] ).

cnf(81,axiom,
    ( skP0(u,v)
    | frontsegP(u,skf44(u,v)) ),
    file('SWC023+1.p',unknown),
    [] ).

cnf(93,axiom,
    ( ~ ssList(u)
    | ~ frontsegP(nil,u)
    | equal(nil,u) ),
    file('SWC023+1.p',unknown),
    [] ).

cnf(128,axiom,
    ( ~ ssList(u)
    | ~ neq(u,nil)
    | ~ frontsegP(skc4,u)
    | ~ frontsegP(skc5,u) ),
    file('SWC023+1.p',unknown),
    [] ).

cnf(188,axiom,
    ( ~ ssList(u)
    | ~ ssList(v)
    | ~ equal(tl(u),tl(v))
    | ~ equal(hd(u),hd(v))
    | equal(u,v)
    | equal(nil,v)
    | equal(nil,u) ),
    file('SWC023+1.p',unknown),
    [] ).

cnf(197,plain,
    ( ~ skP0(skc4,skc5)
    | equal(skc5,skc4) ),
    inference(rew,[status(thm),theory(equality)],[69,68]),
    [iquote('0:Rew:69.1,68.1')] ).

cnf(246,plain,
    ( ~ neq(skc4,nil)
    | ~ frontsegP(skc5,skc4)
    | ~ frontsegP(skc4,skc4) ),
    inference(res,[status(thm),theory(equality)],[2,128]),
    [iquote('0:Res:2.0,128.0')] ).

cnf(281,plain,
    frontsegP(skc4,skc4),
    inference(res,[status(thm),theory(equality)],[2,61]),
    [iquote('0:Res:2.0,61.0')] ).

cnf(282,plain,
    frontsegP(skc4,nil),
    inference(res,[status(thm),theory(equality)],[2,62]),
    [iquote('0:Res:2.0,62.0')] ).

cnf(287,plain,
    ( ~ ssList(u)
    | ~ equal(tl(skc4),tl(u))
    | ~ equal(hd(skc4),hd(u))
    | equal(nil,u)
    | equal(skc4,u)
    | equal(nil,skc4) ),
    inference(res,[status(thm),theory(equality)],[2,188]),
    [iquote('0:Res:2.0,188.1')] ).

cnf(418,plain,
    ( ~ neq(skc5,nil)
    | ~ frontsegP(skc5,skc5)
    | ~ frontsegP(skc4,skc5) ),
    inference(res,[status(thm),theory(equality)],[1,128]),
    [iquote('0:Res:1.0,128.0')] ).

cnf(453,plain,
    frontsegP(skc5,skc5),
    inference(res,[status(thm),theory(equality)],[1,61]),
    [iquote('0:Res:1.0,61.0')] ).

cnf(454,plain,
    frontsegP(skc5,nil),
    inference(res,[status(thm),theory(equality)],[1,62]),
    [iquote('0:Res:1.0,62.0')] ).

cnf(459,plain,
    ( ~ ssList(u)
    | ~ equal(tl(skc5),tl(u))
    | ~ equal(hd(skc5),hd(u))
    | equal(nil,u)
    | equal(skc5,u)
    | equal(nil,skc5) ),
    inference(res,[status(thm),theory(equality)],[1,188]),
    [iquote('0:Res:1.0,188.1')] ).

cnf(547,plain,
    ( ~ frontsegP(skc5,skc4)
    | ~ neq(skc4,nil) ),
    inference(mrr,[status(thm)],[246,281]),
    [iquote('0:MRR:246.2,281.0')] ).

cnf(550,plain,
    ~ frontsegP(skc4,skc5),
    inference(mrr,[status(thm)],[418,13,453]),
    [iquote('0:MRR:418.0,418.1,13.0,453.0')] ).

cnf(561,plain,
    equal(nil,skc5),
    inference(spt,[spt(split,[position(s1)])],[459]),
    [iquote('1:Spt:459.5')] ).

cnf(647,plain,
    frontsegP(skc4,skc5),
    inference(rew,[status(thm),theory(equality)],[561,282]),
    [iquote('1:Rew:561.0,282.0')] ).

cnf(678,plain,
    $false,
    inference(mrr,[status(thm)],[647,550]),
    [iquote('1:MRR:647.0,550.0')] ).

cnf(766,plain,
    ~ equal(nil,skc5),
    inference(spt,[spt(split,[position(sa)])],[678,561]),
    [iquote('1:Spt:678.0,459.5,561.0')] ).

cnf(767,plain,
    ( ~ ssList(u)
    | ~ equal(tl(skc5),tl(u))
    | ~ equal(hd(skc5),hd(u))
    | equal(nil,u)
    | equal(skc5,u) ),
    inference(spt,[spt(split,[position(s2)])],[459]),
    [iquote('1:Spt:678.0,459.0,459.1,459.2,459.3,459.4')] ).

cnf(782,plain,
    equal(nil,skc4),
    inference(spt,[spt(split,[position(s2s1)])],[287]),
    [iquote('2:Spt:287.5')] ).

cnf(785,plain,
    cyclefreeP(skc4),
    inference(rew,[status(thm),theory(equality)],[782,6]),
    [iquote('2:Rew:782.0,6.0')] ).

cnf(786,plain,
    totalorderP(skc4),
    inference(rew,[status(thm),theory(equality)],[782,7]),
    [iquote('2:Rew:782.0,7.0')] ).

cnf(787,plain,
    strictorderP(skc4),
    inference(rew,[status(thm),theory(equality)],[782,8]),
    [iquote('2:Rew:782.0,8.0')] ).

cnf(788,plain,
    totalorderedP(skc4),
    inference(rew,[status(thm),theory(equality)],[782,9]),
    [iquote('2:Rew:782.0,9.0')] ).

cnf(789,plain,
    strictorderedP(skc4),
    inference(rew,[status(thm),theory(equality)],[782,10]),
    [iquote('2:Rew:782.0,10.0')] ).

cnf(790,plain,
    duplicatefreeP(skc4),
    inference(rew,[status(thm),theory(equality)],[782,11]),
    [iquote('2:Rew:782.0,11.0')] ).

cnf(791,plain,
    equalelemsP(skc4),
    inference(rew,[status(thm),theory(equality)],[782,12]),
    [iquote('2:Rew:782.0,12.0')] ).

cnf(797,plain,
    frontsegP(skc5,skc4),
    inference(rew,[status(thm),theory(equality)],[782,454]),
    [iquote('2:Rew:782.0,454.0')] ).

cnf(800,plain,
    ~ equal(skc5,skc4),
    inference(rew,[status(thm),theory(equality)],[782,766]),
    [iquote('2:Rew:782.0,766.0')] ).

cnf(831,plain,
    ( skP0(u,v)
    | neq(skf44(u,v),skc4) ),
    inference(rew,[status(thm),theory(equality)],[782,79]),
    [iquote('2:Rew:782.0,79.1')] ).

cnf(834,plain,
    ( ~ frontsegP(skc5,skc4)
    | ~ neq(skc4,skc4) ),
    inference(rew,[status(thm),theory(equality)],[782,547]),
    [iquote('2:Rew:782.0,547.1')] ).

cnf(854,plain,
    ( ~ ssList(u)
    | ~ frontsegP(nil,u)
    | equal(skc4,u) ),
    inference(rew,[status(thm),theory(equality)],[782,93]),
    [iquote('2:Rew:782.0,93.2')] ).

cnf(882,plain,
    ~ skP0(skc4,skc5),
    inference(mrr,[status(thm)],[197,800]),
    [iquote('2:MRR:197.1,800.0')] ).

cnf(930,plain,
    ~ neq(skc4,skc4),
    inference(mrr,[status(thm)],[834,797]),
    [iquote('2:MRR:834.0,797.0')] ).

cnf(931,plain,
    ( ~ ssList(u)
    | ~ frontsegP(skc4,u)
    | equal(skc4,u) ),
    inference(rew,[status(thm),theory(equality)],[782,854]),
    [iquote('2:Rew:782.0,854.1')] ).

cnf(1012,plain,
    ( ~ ssList(skf44(skc4,u))
    | skP0(skc4,u)
    | equal(skf44(skc4,u),skc4) ),
    inference(res,[status(thm),theory(equality)],[81,931]),
    [iquote('2:Res:81.1,931.1')] ).

cnf(1014,plain,
    ( skP0(skc4,u)
    | equal(skf44(skc4,u),skc4) ),
    inference(ssi,[status(thm)],[1012,52,2,785,786,787,788,789,790,791]),
    [iquote('2:SSi:1012.0,52.0,2.0,785.0,786.0,787.0,788.0,789.0,790.0,791.0')] ).

cnf(1017,plain,
    ( skP0(skc4,u)
    | skP0(skc4,u)
    | neq(skc4,skc4) ),
    inference(spr,[status(thm),theory(equality)],[1014,831]),
    [iquote('2:SpR:1014.1,831.1')] ).

cnf(1021,plain,
    ( skP0(skc4,u)
    | neq(skc4,skc4) ),
    inference(obv,[status(thm),theory(equality)],[1017]),
    [iquote('2:Obv:1017.0')] ).

cnf(1022,plain,
    skP0(skc4,u),
    inference(mrr,[status(thm)],[1021,930]),
    [iquote('2:MRR:1021.1,930.0')] ).

cnf(1023,plain,
    $false,
    inference(unc,[status(thm)],[1022,882]),
    [iquote('2:UnC:1022.0,882.0')] ).

cnf(1026,plain,
    ~ equal(nil,skc4),
    inference(spt,[spt(split,[position(s2sa)])],[1023,782]),
    [iquote('2:Spt:1023.0,287.5,782.0')] ).

cnf(1027,plain,
    ( ~ ssList(u)
    | ~ equal(tl(skc4),tl(u))
    | ~ equal(hd(skc4),hd(u))
    | equal(nil,u)
    | equal(skc4,u) ),
    inference(spt,[spt(split,[position(s2s2)])],[287]),
    [iquote('2:Spt:1023.0,287.0,287.1,287.2,287.3,287.4')] ).

cnf(1033,plain,
    ~ skP0(skc4,skc5),
    inference(mrr,[status(thm)],[69,1026]),
    [iquote('2:MRR:69.1,1026.0')] ).

cnf(2027,plain,
    ( ~ ssList(skf44(u,skc5))
    | ~ neq(skf44(u,skc5),nil)
    | ~ frontsegP(skc4,skf44(u,skc5))
    | skP0(u,skc5) ),
    inference(res,[status(thm),theory(equality)],[80,128]),
    [iquote('0:Res:80.1,128.3')] ).

cnf(6204,plain,
    ( ~ neq(skf44(u,skc5),nil)
    | ~ frontsegP(skc4,skf44(u,skc5))
    | skP0(u,skc5) ),
    inference(ssi,[status(thm)],[2027,52,1]),
    [iquote('0:SSi:2027.0,52.0,1.0')] ).

cnf(6205,plain,
    ( ~ frontsegP(skc4,skf44(u,skc5))
    | skP0(u,skc5) ),
    inference(mrr,[status(thm)],[6204,79]),
    [iquote('0:MRR:6204.0,79.1')] ).

cnf(7356,plain,
    ( skP0(skc4,skc5)
    | skP0(skc4,skc5) ),
    inference(res,[status(thm),theory(equality)],[81,6205]),
    [iquote('0:Res:81.1,6205.0')] ).

cnf(7357,plain,
    skP0(skc4,skc5),
    inference(obv,[status(thm),theory(equality)],[7356]),
    [iquote('0:Obv:7356.0')] ).

cnf(7358,plain,
    $false,
    inference(mrr,[status(thm)],[7357,1033]),
    [iquote('2:MRR:7357.0,1033.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SWC023+1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n011.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Sun Jun 12 06:46:17 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 3.33/3.57  
% 3.33/3.57  SPASS V 3.9 
% 3.33/3.57  SPASS beiseite: Proof found.
% 3.33/3.57  % SZS status Theorem
% 3.33/3.57  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 3.33/3.57  SPASS derived 4713 clauses, backtracked 1252 clauses, performed 72 splits and kept 3366 clauses.
% 3.33/3.57  SPASS allocated 104398 KBytes.
% 3.33/3.57  SPASS spent	0:00:03.11 on the problem.
% 3.33/3.57  		0:00:00.04 for the input.
% 3.33/3.57  		0:00:00.07 for the FLOTTER CNF translation.
% 3.33/3.57  		0:00:00.05 for inferences.
% 3.33/3.57  		0:00:00.04 for the backtracking.
% 3.33/3.57  		0:00:02.73 for the reduction.
% 3.33/3.57  
% 3.33/3.57  
% 3.33/3.57  Here is a proof with depth 2, length 68 :
% 3.33/3.57  % SZS output start Refutation
% See solution above
% 3.33/3.57  Formulae used in the proof : co1 ax17 ax60 ax62 ax64 ax66 ax69 ax72 ax74 ax42 ax45 ax46 ax77
% 3.33/3.57  
%------------------------------------------------------------------------------